English grammar issues about praying for the weather

The three expressions, with three different levels of correctness and meaning, are not the same.

1. What's the weather like?

What is a pronoun and serves as the object of the following preposition like.

is is the linking verb

the weather is the subject

like a preposition, preposition + pronoun serve as a predicate.

This sentence asks about the characteristics of the weather, such as whether it is tropical or cold zone, warm in winter and cool in summer, humid, or cold and dry.

2. How's the weather?

How is an adverb, used as a predicate.

is is the linking verb

the weather is the subject

This sentence asks about the state of the weather, such as whether it is raining or sunny, cold or hot.

3. How's the weather like?

The grammar of this sentence is wrong. How can only be an adverb in this context, like can only be a preposition, and adverbs cannot be the objects of prepositions. It's just that Americans use this sentence pattern everywhere, and they should have corrupted what into how.

This may be considered a convention, right? The meaning of this sentence should be closer to What's the weather like? Such as:

How's the weather like in Houston? How is the weather in Houston?